An Exact Algorithm for Any-flavor Lattice QCD with Kogut-Susskind Fermion

TL;DR

This paper introduces an exact simulation algorithm for lattice QCD with Kogut-Susskind fermions, extending the PHMC method to handle any number of flavors through polynomial approximation and correction techniques.

Contribution

The authors develop an extension of the PHMC algorithm that efficiently handles fractional powers of the KS fermion operator for any flavor number, enabling exact dynamical QCD simulations.

Findings

Successfully tested on a 16^4 lattice with realistic quark mass ratios.

Confirmed the algorithm's validity and practical feasibility through numerical simulations.

Demonstrated the algorithm's potential as an exact method for dynamical QCD with KS fermions.

Abstract

We propose an exact simulation algorithm for lattice QCD with dynamical Kogut-Susskind fermion in which the N_f-flavor fermion operator is defined as the N_f/4-th root of the Kogut-Susskind (KS) fermion operator. The algorithm is an extension of the Polynomial Hybrid Monte Carlo (PHMC) algorithm to KS fermions. The fractional power of the KS fermion operator is approximated with a Hermitian Chebyshev polynomial, with which we can construct an algorithm for any number of flavors. The error which arises from the approximation is corrected by the Kennedy-Kuti noisy Metropolis test. Numerical simulations are performed for the two-flavor case for several lattice parameters in order to confirm the validity and the practical feasibility of the algorithm. In particular tests on a 16^4 lattice with a quark mass corresponding to m_{PS}/m_V ~ 0.68 are successfully accomplished. We conclude that our algorithm provides an attractive exact method for dynamical QCD simulations with KS fermions.